The major challenge of current Strapdown Inertial Naviagtion System/Celestial Navigation System (SINS/CNS) integrated systems is navigation accuracy degradation due to the failure to accurately estimate the accelerometer bias even when using stellar refraction information (e.g. the number of refraction stars is less than three). To solve this problem, this paper presents a new method for improving the accuracy of the traditional inertial-based integrated systems installed on ballistic vehicles. In an analogy with nonholonomic constraints in land navigation, this algorithm exploits the constraints that govern the motion of a ballistic vehicle in the free flight phase to obtain accelerometer bias observations. Improvements in dynamic equations are used to reduce the propagation of navigation errors, and high-rate virtual constraints are used to reduce the impact of bias errors. An information filter is devised to fuse the multi-rate observations from multiple sources, i.e. SINS, CNS and model constraints. The proposed method is also evaluated by long-range ballistic vehicle navigation simulations. The results indicate that the proposed constrained algorithm can address the degradation problem with remarkable accuracy improvements without adding extra sensors, enhancing the SINS-based navigation performance for ballistic applications.

In recent years, navigation by stellar refraction has received considerable attention, having advantages of high accuracy, simple construction, and low cost. Nevertheless, there are many limitations to the precision and application of this method using a traditional measurement model. This article studies the changing pattern of atmospheric density, the disturbed atmospheric density model and measurement model of stellar refraction ranging from 20 km to 50 km. Furthermore, a control algorithm of multiple mode switching and an adaptive measurement model are proposed. With this method, any refracted starlight from the scope of between 20 km and 50 km can be captured and the measurement model at the appropriate height can be automatically established. Due to this, the reliability and practicality of navigation have been raised considerably. Accuracy of navigation using the adaptive measurement method is observed to improve by about 14%, using computer simulation based on an Unscented Kalman Filter (UKF).